4 papers
On Boundary Crossing Probabilities for Diffusion Processes
Konstantin A. Borovkov, Andrew N. Downes
In this paper, we establish a relationship between the asymptotic form of conditional boundary crossing probabilities and first passage time densities for diffusion processes. Name…
On exit times of Levy-driven Ornstein--Uhlenbeck processes
K. Borovkov, A. Novikov
We prove two martingale identities which involve exit times of Levy-driven Ornstein--Uhlenbeck processes. Using these identities we find an explicit formula for the Laplace transfo…
On the ruin time distribution for a Sparre Andersen process with exponential claim sizes
K. A. Borovkov, D. C. M. Dickson
We derive a closed-form (infinite series) representation for the distribution of the ruin time for the Sparre Andersen model with exponentially distributed claims. This extends a r…
First Passage Densities and Boundary Crossing Probabilities for Diffusion Processes
A. N. Downes, K. Borovkov
We consider the boundary crossing problem for time-homogeneous diffusions and general curvilinear boundaries. Bounds are derived for the approximation error of the one-sided (upper…